So the garage is single skin brick and can effectively be regarded as an extension to the house. The wall between house and garage is uninsulated. After works are complete and the garage has become a playroom it will be a part of the house like any other, and the temperature in the playroom will be the same as that in the house, so the effective temperature drop across the wall will be 0 degrees
You want the lowest U value, hang the cost or complications to building this will bring. The wall will be insulated internally and another wall constructed
Personally, I'd render the existing skin with a non waterproof render on the inside, then line it with 100mm of PIR insulation. The purpose of the render is to seal up gaps and cracks that leak air, but still allows a path for moisture to take out of the wall.
After that, construct a lightweight timber frame wall 90mm wide, sitting on a small block or brick upstand and a dpc. It's lighter and faster to construct than a masonry leaf. The timber frame panels can be filled with 50mm of PIR or 90mm of mineral wool. You can then line the internal face with OSB, run a breather membrane such as tyvek airguard over the OSB and seal it together to reduce the opportunity for draughts to nil. The purpose of the OSB is to provide a surface to fit the membranes to, afford them some protection against plasterboard hole making activities (using a blunt pointed saw) and it provides a surface to mount electric boxes etc to
Add 25mm battens over the top of this, and use them to mechanically fix the joints in the airguard (which will be glued) as well as at other points along the wall (600mm spacings). Run your services in the void created and then hang your plasterboard. The tyvek can be ordered reflective, and in combination with the service void cavity has a minor improvement in U.
This wall construction would have a U around 0.14 and give you something to hang your internal stuff on/in at the loss of 65mm over just lining the wall with 150mm of PIR backed plasterboard achieves the same U but isn't as airtight and has nowhere to run services/hang shelves etc.
You reach a point with insulating where it isn't worth throwing the money at insulation without making efforts to improve the air tightness. 500mm of kingspan standing up in the garden is going to do nothing to keep your house warm
Also, for reference purposes, a house built to Passivhaus standards must achieve a wall U value of 0.15 or better. British building regs is 0.30 or better